Hyperpolarizability tensors, molecular

Heterogeneous dielectric media models have included the developments of Jprgensen et al. [7-9] (reviewed here) and Corni and Tomasi [52,53], Generally, the number of methods for determining frequency-dependent molecular electronic properties, such as the polarizability or first- and second hyperpolarizability tensors of heterogeneously solvated molecules, is very limited. 

Our present focus is on correlated electronic structure methods for describing molecular systems interacting with a structured environment where the electronic wavefunction for the molecule is given by a multiconfigurational self-consistent field wavefunction. Using the MCSCF structured environment response method it is possible to determine molecular properties such as (i) frequency-dependent polarizabilities, (ii) excitation and deexcitation energies, (iii) transition moments, (iv) two-photon matrix elements, (v) frequency-dependent first hyperpolarizability tensors, (vi) frequency-dependent polarizabilities of excited states, (vii) frequency-dependent second hyperpolarizabilities (y), (viii) three-photon absorptions, and (ix) two-photon absorption between excited states. 

Based on the MCSCF/CM quadratic response method it is possible to calculate the hyperpolarizability tensor and the two-photon absorption cross-sections. The calculated MCSCF/CM properties exhibit for all the individual tensor components substantial shifts compared with the corresponding molecular properties of the molecule in vacuum. 

For dipolar chromophores that are the subject of this chapter, only one component of the molecular hyperpolarizability tensor, Pzzz, is important. Thus, the summation in Eq. (8) disappears. Electric field poling induces Cv cylindrical polar symmetry. Assuming Kleinman [12] symmetry, only two independent components of the macroscopic second-order nonlinear optical susceptibility tensor... 

As will be explained in Section 8.3.3, the reduction spectrum of rank-three tensors contains, in the general case, one (pseudo)scalar, three vectors, two (pseudo)devia-tors, and one septor [13]. Here, we only have to deal with the vectorial parts. They transform as a vector. Hence, the scalar product of the dipole moment vector with a vector part of the first hyperpolarizability tensor can be written as the simple product of two scalars, when we designate 9 as the angle between the molecular axis (z-axis) and the dipole moment axis (Eq. (14)). 

These relations between the experimental observable in EFISHG, p., and the molecular third-rank hyperpolarizability tensor components do not reflect the (approximate) symmetry of the molecule yet. When we accept (approximate) C21, symmetry for a molecule with a planar conjugated r-electron system (in the xz-plane), we are still left with these three non-zero and independent tensor components. 

It is important to make the distinction, and state the exact relation, between the measured observable and the actual hyperpolarizability tensor component(s), even if, for specific experimental conditions and molecular symmetries, their values turn out to be identical. What is also important is the fact that only one experimental condition is favorable for EFISHG, namely parallel polarizations for all optical and static fields. This leads to only one observable, resulting in only a single value to be deduced. It is not possible with EFISHG to determine more than one tensor component hence, one often contends either with the approximation that P. was determined, or with the statement that / , was obtained, in any of the above-mentioned relations to the individual tensor components. Even then, the assumption that the dipole moment vector and the vector part of the third-rank tensor along the molec-... 

In addition to this enhancement, several other effects can be induced by the new conformation at the microscopic scale, such as the appearance of olf-diagonal molecular hyperpolarizability tensor components. The study of these microscopically aligned molecules has also provided new fundamental insights and was only made possible through creative synthetic chemistry. The systems that have been studied so far include dimers and tetramers such as the binaphthyl ethers and the calixarenes, and polymers with rigid backbones that force the pendant D ti-A chromophores into a non-centrosymmetric conformation. 

To understand and optimize the electro-optic properties of polymers by the use of molecular engineering, it is of primary importance to be able to relate their macroscopic properties to the individual molecular properties. Such a task is the subject of intensive research. However, simple descriptions based on the oriented gas model exist [ 20,21 ] and have proven to be in many cases a good approximation for the description of poled electro-optic polymers [22]. The oriented gas model provides a simple way to relate the macroscopic nonlinear optical properties such as the second-order susceptibility tensor elements expressed in the orthogonal laboratory frame X,Y,Z, and the microscopic hyperpolarizability tensor elements that are given in the orthogonal molecular frame x,y,z (see Fig. 9). 

In the present contribution we will discuss the direction of the changes of the NLO response and the solvatochromic behavior as a function of solvent polarity of the D-tt-A chromophores. The best starting point for these considerations seems to be the simple two-state model for the first-order hyperpolarizability (/ ) [8]. To avoid the extreme complexity of the sum-over-states (SOS) expression [101], Oudar and Chemla proposed the relation between the dominant component of 13 along the molecular axis (let it be the x-axis) and the spectroscopic parameters of the low-lying CT transition [8]. The use of the two-level approximation in the static case (ru = 0.0) has lead to the following expression for the static component of the first-order hyperpolarizability tensor ... 

In formula (34), /u, (f) = (0 /Ai(f) 0 ) is the ground state, permanent, electric dipole moment of species f, while ) is the molecular first hyperpolarizability tensor defined by... 

Maroulis126 has also investigated the static hyperpolarizability tensor (y) by the finite field method. The molecular geometries and levels of correlated calculation are as in reference 125, although in this case some very large basis... 

In order to obtain a useful material possessing a large second order nonlinear susceptibility tensor % 2) one needs to use molecules with a large microscopic second order nonlinear hyperpolarizability tensor B organised in such a way that the resulting system has no centre of symmetry and an optimized constructive additivity of the molecular hyperpolarizabilities. In addition, the ordered structure thus obtained must not loose its nonlinear optical properties with time. The nonlinear optical (NLO) active moieties which have been synthesized so far are derived from the donor-rc system-acceptor molecular concept (Figure 1). 

The HRS technique [25-27] involves the detection of the incoherently scattered second harmonic generated by the molecule in solution under irradiation with a laser of wavelength 2, leading to the mean value of the x tensor product. By analysis of the polarization dependence of the second harmonic signal, which can be evaluated selecting the polarization of the incident and scattered radiation, it is possible to obtain information about the single components of the quadratic hyperpolarizability tensor jS. Unlike EFISH, HRS can also be used for ionic molecular species and for nondipolar molecules such as ocmpolar molecules. In this chapter, the quadratic hyperpolarizability measured with an incident wavelength 2 by the EFISH and HRS techniques will be indicated as /l i(EFISH) and / (HRS), respectively. 

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